Let Ab, Ac be the orthogonal projections of the vertex  A  on the bisectors and define analogously Bc, Ba, Ca, Cb.  The perpendicular bisectors of AbAc, BcBA, CaCb are concurrent. If the midpoints oof AbAc, BcBa, CaCb  are Ma, Mb, Mc the triangles ABC, MaMbMc are orthologic; the orthologic centers are X(84) and the midpoint between the incenter I and the orthocenter H.